Forest: Thanks for confirming that my matrix for determining the Kemeny outcome for 3 candidates is correct. Now, is Kemeny's Rule, as defined by my matrix for 3 candidate tallies, the same as the Condorcet method which is described on the EM website <http://electionmethods.org/>?
SB --- In [EMAIL PROTECTED], Forest Simmons <[EMAIL PROTECTED]> wrote: > Your example is correctly done. > > Despite the intractability of the method for large numbers of candidates, > it seems like an ideal method for some situations. > > One application could be in choosing between several orders that have been > found by other means. > > [The main computational difficulty of finding the Kemeny order is not in > calculating the mean Kemeny distance to any particular order, but in the > sheer magnitude of the number of possible orders.] > > Here's a homely example: > > Start with the candidates ranked by Approval, Borda, Ranked Pairs, etc. > > Do both a sink sort and a bubble sort to each of these preliminary orders. > > [These sortings are ways of achieving "local Keminization." Ranked Pairs > is already locally Kemeny optimal.] > > See which of the resulting locally optimum orders is best (among those > considered) globally by calculating the mean distance of each to the > preference orders on the ballots. > > Forest > > On Fri, 20 Dec 2002, barnes99 wrote: > > > Here is my matrix for Kemeny's Rule with 3 candidates. Please let me know if I > > got it right or wrong. > > > > Here is an example of a Kemeny Rule tally for profile p, p=(1,1,0,0,0,0), > > where the first thru sixth columns represent, respectively, the number of ABC, > > ACB, CAB, CBA, BCA, and BAC voters. > > > > Voting Vector: > > > > p=[ 1 1 0 0 0 0 ] > > > > Matrix (M) for Kemeny's Rule: > > > > [[ 0 1 2 3 2 1 ] > > [ 1 0 1 2 3 2 ] > > [ 2 1 0 1 2 3 ] > > [ 3 2 1 0 1 2 ] > > [ 2 3 2 1 0 1 ] > > [ 1 2 3 2 1 0 ]] > > > > > > The KR tally is: > > > > p(M)=[ 1 1 3 5 5 3 ], where > > > > ABC=[0+1+0+0+0+0]=1 > > ACB=[1+0+0+0+0+0]=1 > > CAB=[2+1+0+0+0+0]=3 > > CBA=[3+2+0+0+0+0]=5 > > BCA=[2+3+0+0+0+0]=5 > > BAC=[1+2+0+0+0+0]=3 > > > > > > This is the measure of the "distance" from unanimity, so the lower the score > > the better. In this example, we have a tie between the ABC and ACB outcomes, > > in which case I guess the final outcome must be A>B~C. This may not be a very > > interesting example, but the point is that I believe this is how to do a KR > > tally with 3 candidates. Please correct me, if I'm wrong. > > > > > > > > Thank you, > > SB Steve Barney Richard M. Hare, 1919 - 2002, In Memoriam: <http://www.petersingerlinks.com/hare.htm>. Did you know there is an web site where, if you click on a button, the advertisers there will donate 2 1/2 cups of food to feed hungry people in places where there is a lot of starvation? See: <http://www.thehungersite.com>. ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
